Problem: Solve for $x$ and $y$ using elimination. ${5x-3y = -7}$ ${-4x+3y = 11}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {5x-3y = -7}\thinspace$ to find $y$ ${5}{(4)}{ - 3y = -7}$ $20-3y = -7$ $20{-20} - 3y = -7{-20}$ $-3y = -27$ $\dfrac{-3y}{{-3}} = \dfrac{-27}{{-3}}$ ${y = 9}$ You can also plug ${x = 4}$ into $\thinspace {-4x+3y = 11}\thinspace$ and get the same answer for $y$ : ${-4}{(4)}{ + 3y = 11}$ ${y = 9}$